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{\bf Assigment 1}
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The assigments are meant to encourage you to test by yourself
some of the things that we discuss in class.

1) 
Here we touch the thorny issue of high level vs low level
languages.

We will compare the time it takes to evaluate the average
of n random numbers in mathematica (or maple or any other
high level language of your choice )  and in fortran.
Play with the parameter n ( size of the set that you average),
and find out  at which values of n, you can see noticeable
differences between the  programs written in two lanaguages.


2) 
Here we would like you to  get a feeling for roundoff errors in
numerical differntiation.  Estimate the  value of the derivative
of  cos(x) at x=1. Discuss  the  value of h  required
in your finite difference approximation scheme. 
Try double precision.

Can you suggest a way of obtaining a more precise answer with
the data you already have ?




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